There seems to be some confusion about this, but in fact only the big spiders with the round belly count towards the achievement:

I do not recommend to try this achievement in the last battle, as it tends to be quite hectic and you also waste lots of fuel on the stinger spiders (the ones that look like scorpions).

Instead pick the stage / layer below the last one. You will notice, that lots of those fat belly bastards climb out of holes and run along the walls - in fact, I think that their amounts are infinite. I just stood in front of the same hole and burned them all with my flamethrower until the achievement popped up.

Yes.